The electronic-structure problem considers electrons interacting with each other and some fixed nuclei. An efficient simulation of such systems could help understand chemical reactions, and provide insight into material properties. Here, we consider representing the electronic-structure Hamiltonian in the plane-wave basis [1]}:
\(\begin{aligned}H&=\frac{1}{2n}\sum _{j,k,\mu }\kappa _{\mu }^2\cos [\kappa _{\mu }\cdot r_{k-j}]A_{j}^\dagger A_{k}\\&\quad -\frac{4\pi }{\omega }\sum _{j,\iota ,\mu \ne 0}\frac{\zeta _\iota \cos [\kappa _{\mu }\cdot (\widetilde{r}_\iota -r_j)]}{\kappa _{\mu }^2}N_{j}+\frac{2\pi }{\omega }\sum _{\begin{array}{c}j\ne k\\\mu \ne 0\end{array}}\frac{\cos [\kappa _{\mu }\cdot r_{j-k}]}{\kappa _{\mu }^2}N_{j}N_{k},\end{aligned}\) 
